In an update to the market today (October 12) the firm said the change came as he prepared to take up a new role within Jupiter focusing on it stewardship and corporate responsibility activities.
Mr Bonham Carter, who stepped down as chief executive in 2014, will leave the board after Jupiter's annual general meeting next year.
Jupiter said the shake up would allow him "greater flexibility" to manage his portfolio of external appointments.
Mr Bonham Carter, who has worked at Jupiter for 26 years, will now assume the chairmanship of both Jupiter's stewardship committee and its corporate and social responsibility committee with immediate effect.
The former chief executive said now was a good time to step down from the board to allow him to "focus on other interests".
He added: "However, I am pleased to be able to remain involved with Jupiter, working closely with the existing experienced team to provide a strong voice on a subject that understandably continues to grow in importance to our clients.
"At a time of major societal, political and economic change brought about by the Covid-19 pandemic, there has never been a better time to demonstrate both the financial benefit and wider value of active asset management. I very much look forward to focusing on this when I take up my new role."
Mr Bonham Carter was appointed as chief investment officer at Jupiter in 1999 before becoming joint chief executive in 2000 and subsequently group chief executive in 2007 before heading up the company's management buyout and its IPO in June 2010.
Nichola Pease, chairwoman of Jupiter, commented: "Edward has devoted over 25 years of service to Jupiter, leading the company through some of the most important milestones in its history including our IPO.
"Among his many contributions to Jupiter, he has championed the role of responsible investing and I am delighted that we will continue to benefit from his significant expertise in this area."
Jupiter said Mr Bonham Carter would continue to be "actively involved" in meeting with its investee companies and contributing to engagement and policy work.
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